Problem: Is ${129809}$ divisible by $4$ ?
Explanation: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{1298} {09} = \gray{1298} \gray{00} + {09} $ Because $129800$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${9}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $9$ , divisible by $4$ No, $9$ is not divisible by $4$, so $129809$ is also not divisible by $4$.